K-theory of Jones polynomials
Andrey Glubokov, Igor Nikolaev
TL;DR
This paper demonstrates how the Jones polynomials of knots and links can be derived from the K-theory of a specific cluster C*-algebra associated with a sphere with two cusps, exploring connections with Chebyshev polynomials.
Contribution
It introduces a novel approach linking Jones polynomials to the K-theory of cluster C*-algebras, revealing new algebraic structures underlying knot invariants.
Findings
Jones polynomials recovered from K-theory of cluster C*-algebra
Interplay between Chebyshev and Jones polynomials analyzed
New algebraic perspective on knot invariants provided
Abstract
We recover the Jones polynomials of knots and links from the K-theory of a cluster C*-algebra of the sphere with two cusps. In particular, an interplay between the Chebyshev and Jones polynomials is studied.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research